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The absence of eigenvalues for certain operators with partially periodic coefficients 某些部分周期系数算子的特征值不存在
IF 0.8 4区 数学 Q2 MATHEMATICS Pub Date : 2022-08-24 DOI: 10.1090/spmj/1730
N. Filonov

The absence of eigenvalues is proved for the Schrödinger operator Δ + V ( x , y ) -Delta + V(x,y) in the Euclidean space whose potential is periodic in some variables and decays in the remaining variables faster than power 1 1 . A similar result for the Maxwell operator is established.

证明了欧氏空间中Schrödinger算子−Δ+V(x,y)-Δ+V。建立了麦克斯韦算子的类似结果。
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引用次数: 1
Limit behavior of Weyl coefficients Weyl系数的极限行为
IF 0.8 4区 数学 Q2 MATHEMATICS Pub Date : 2022-08-24 DOI: 10.1090/spmj/1729
R. Pruckner, H. Woracek
<p>The sets of radial or nontangential limit points towards <inline-formula content-type="math/mathml"><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="i normal infinity"> <mml:semantics> <mml:mrow> <mml:mi>i</mml:mi> <mml:mi mathvariant="normal">∞<!-- ∞ --></mml:mi> </mml:mrow> <mml:annotation encoding="application/x-tex">iinfty</mml:annotation> </mml:semantics></mml:math></inline-formula> of a Nevanlinna function <inline-formula content-type="math/mathml"><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="q"> <mml:semantics> <mml:mi>q</mml:mi> <mml:annotation encoding="application/x-tex">q</mml:annotation> </mml:semantics></mml:math></inline-formula> are studied. Given a nonempty, closed, and connected subset <inline-formula content-type="math/mathml"><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="script upper L"> <mml:semantics> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi class="MJX-tex-caligraphic" mathvariant="script">L</mml:mi> </mml:mrow> </mml:mrow> <mml:annotation encoding="application/x-tex">{mathcal {L}}</mml:annotation> </mml:semantics></mml:math></inline-formula> of <inline-formula content-type="math/mathml"><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="double-struck upper C Subscript plus Baseline overbar"> <mml:semantics> <mml:mover> <mml:msub> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi mathvariant="double-struck">C</mml:mi> </mml:mrow> </mml:mrow> <mml:mo>+</mml:mo> </mml:msub> <mml:mo accent="false">¯<!-- ¯ --></mml:mo> </mml:mover> <mml:annotation encoding="application/x-tex">overline {{mathbb {C}}_+}</mml:annotation> </mml:semantics></mml:math></inline-formula>, a Hamiltonian <inline-formula content-type="math/mathml"><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper H"> <mml:semantics> <mml:mi>H</mml:mi> <mml:annotation encoding="application/x-tex">H</mml:annotation> </mml:semantics></mml:math></inline-formula> is constructed explicitly such that the radial and outer angular cluster sets towards <inline-formula content-type="math/mathml"><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="i normal infinity"> <mml:semantics> <mml:mrow> <mml:mi>i</mml:mi> <mml:mi mathvariant="normal">∞<!-- ∞ --></mml:mi> </mml:mrow> <mml:annotation encoding="application/x-tex">iinfty</mml:annotation> </mml:semantics></mml:math></inline-formula> of the Weyl coefficient <inline-formula content-type="math/mathml"><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="q Subscript upper H"> <mml:semantics> <mml:msub> <mml:mi>q</mml:mi> <mml:mi>H</mml:mi> </mml:msub> <mml:annotation encoding="application/x-tex">q_H</mml:a
研究了Nevanlinna函数q q向i∞i infty方向的径向或非切向极限点集。给定一个非空的、封闭的、连通的子集L {mathcal L{ (C +¯}}overline{{mathbb C_{+)}}明确地构造了一个哈密顿量H H,使得Weyl系数q H q_H向i∞i }infty方向的径向和外角簇集都等于L {mathcal L{。该方法是基于对所有哈密顿算子集合上的重标算子的连续群作用的研究。}}
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引用次数: 1
On a mathematical model of a repressilator 关于阻遏物的数学模型
IF 0.8 4区 数学 Q2 MATHEMATICS Pub Date : 2022-08-24 DOI: 10.1090/spmj/1727
S. Glyzin, A. Kolesov, N. Rozov
A mathematical model of the simplest three-link oscillatory gene network, the so-called repressilator, is considered. This model is a nonlinear singularly perturbed system of three ordinary differential equations. The existence and stability of a relaxation periodic solution invariant with respect to cyclic permutations of coordinates are investigated for this system.
考虑了一个最简单的三连杆振荡基因网络的数学模型,即所谓的阻遏物。该模型是一个由三个常微分方程组成的非线性奇摄动系统。研究了该系统关于坐标循环排列的松弛周期解不变量的存在性和稳定性。
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引用次数: 0
Banach limits: extreme properties, invariance and the Fubini theorem 巴拿赫极限:极值性质、不变性和富比尼定理
IF 0.8 4区 数学 Q2 MATHEMATICS Pub Date : 2022-06-27 DOI: 10.1090/spmj/1717
N. Avdeev, E. Semenov, A. Usachev
A Banach limit on the space of all bounded real sequences is a positive normalized linear functional that is invariant with respect to the shift. The paper studies such properties of Banach limits as multiplicativity and the validity of Fubini’s theorem. A subset of Banach limits invariant with respect to dilation operators is also treated.
所有有界实序列空间上的Banach极限是一个正的归一化线性泛函,它对位移是不变的。本文研究了Banach极限的乘法性和富比尼定理的有效性。还讨论了关于扩张算子的Banach极限不变量的一个子集。
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引用次数: 1
The set of zeros of the Riemann zeta function as the point spectrum of an operator 作为算子的点谱的黎曼函数的零的集合
IF 0.8 4区 数学 Q2 MATHEMATICS Pub Date : 2022-06-27 DOI: 10.1090/spmj/1720
V. Kapustin

A possible way of proving the Riemann hypothesis consists of constructing a selfadjoint operartor whose spectrum coincides with the set { z : | Im z | > 1 2 ,   ζ ( 1 2 i z ) = 0 } {z,: , |operatorname {Im}z|>frac 12, zeta big (frac {1}{2}-izbig )=0} . In the paper we construct a rank-one perturbation of a selfadjoint operator related to a certain canonical system for which a similar property is fulfilled.

证明黎曼假说的一种可能的方法是构造一个自伴操纵子,其谱与集合{z:|Im一致⁡ z|>12,ζ(12−i z)=0}{z,:,|运算符名称{Im}z|>frac 12,zetabig(frac{1}{2}-izbig)=0}。在本文中,我们构造了一个自伴随算子的秩一微扰,它与一个具有相似性质的正则系统有关。
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引用次数: 0
Weighted string equation where the weight is a noncompact multiplier: continuous spectrum and eigenvalues 权重为非紧乘数的加权字符串方程:连续谱和特征值
IF 0.8 4区 数学 Q2 MATHEMATICS Pub Date : 2022-06-27 DOI: 10.1090/spmj/1723
E. B. Sharov, I. Sheipak
The oscillation equation for a singular string with discrete weight generated by a self-similar n n -link multiplier in the Sobolev space with a negative smoothness index is considered. It is shown that in the case of a noncompact multiplier, the string problem is equivalent to the spectral problem for an ( n − 1 ) (n-1) -periodic Jacobi matrix. In the case of n = 3 n=3 , a complete description of the spectrum of the problem is given, and a criterion for emergence of an eigenvalue in a gap of the continuous spectrum is obtained.
研究了Sobolev空间中具有负光滑指数的自相似n-n链乘法器生成的离散权奇异弦的振动方程。结果表明,在非紧乘法器的情况下,串问题等价于(n-1)(n-1的)周期Jacobi矩阵的谱问题。在n=3n=3的情况下,给出了该问题的谱的完整描述,并得到了在连续谱的间隙中出现特征值的判据。
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引用次数: 0
Projective free algebras of bounded holomorphic functions on infinitely connected domains 无限连通域上有界全纯函数的射影自由代数
IF 0.8 4区 数学 Q2 MATHEMATICS Pub Date : 2022-06-27 DOI: 10.1090/spmj/1718
A. Brudnyi
<p>The algebra <inline-formula content-type="math/mathml"><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper H Superscript normal infinity Baseline left-parenthesis upper D right-parenthesis"> <mml:semantics> <mml:mrow> <mml:msup> <mml:mi>H</mml:mi> <mml:mi mathvariant="normal">∞<!-- ∞ --></mml:mi> </mml:msup> <mml:mo stretchy="false">(</mml:mo> <mml:mi>D</mml:mi> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> <mml:annotation encoding="application/x-tex">H^infty (D)</mml:annotation> </mml:semantics></mml:math></inline-formula> of bounded holomorphic functions on <inline-formula content-type="math/mathml"><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper D subset-of double-struck upper C"> <mml:semantics> <mml:mrow> <mml:mi>D</mml:mi> <mml:mo>⊂<!-- ⊂ --></mml:mo> <mml:mrow class="MJX-TeXAtom-ORD"> <mml:mi mathvariant="double-struck">C</mml:mi> </mml:mrow> </mml:mrow> <mml:annotation encoding="application/x-tex">Dsubset mathbb {C}</mml:annotation> </mml:semantics></mml:math></inline-formula> is projective free for a wide class of infinitely connected domains. In particular, for such <inline-formula content-type="math/mathml"><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper D"> <mml:semantics> <mml:mi>D</mml:mi> <mml:annotation encoding="application/x-tex">D</mml:annotation> </mml:semantics></mml:math></inline-formula> every rectangular left-invertible matrix with entries in <inline-formula content-type="math/mathml"><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper H Superscript normal infinity Baseline left-parenthesis upper D right-parenthesis"> <mml:semantics> <mml:mrow> <mml:msup> <mml:mi>H</mml:mi> <mml:mi mathvariant="normal">∞<!-- ∞ --></mml:mi> </mml:msup> <mml:mo stretchy="false">(</mml:mo> <mml:mi>D</mml:mi> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> <mml:annotation encoding="application/x-tex">H^infty (D)</mml:annotation> </mml:semantics></mml:math></inline-formula> can be extended in this class of matrices to an invertible square matrix. This follows from a new result on the structure of the maximal ideal space of <inline-formula content-type="math/mathml"><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="upper H Superscript normal infinity Baseline left-parenthesis upper D right-parenthesis"> <mml:semantics> <mml:mrow> <mml:msup> <mml:mi>H</mml:mi> <mml:mi mathvariant="normal">∞<!-- ∞ --></mml:mi> </mml:msup> <mml:mo stretchy="false">(</mml:mo> <mml:mi>D</mml:mi> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> <mml:annotation encoding="application/x-tex">H^infty (D)</mml:annotation> </mml:semantics></mml:math></inline-formula> asserting that its covering dimension is <inl
D⊂C Dsubet mathbb{C}上有界全纯函数的代数H∞(D)H^infty(D)对于一大类无限连通域是无投影的。特别地,对于这样的D D,每一个在H∞(D)H^infty(D)中有项的矩形左可逆矩阵都可以在这类矩阵中推广为可逆平方矩阵。这源于关于H∞(D)H^infty(D)的最大理想空间结构的一个新结果,该结果断言其覆盖维数为2,并且第二Čech上同调群是平凡的。
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引用次数: 2
Preservation of classes of entire functions defined in terms of growth restrictions along the real axis under perturbations of their zero sets 在零集扰动下,用实轴生长限制定义的整函数类的保存
IF 0.8 4区 数学 Q2 MATHEMATICS Pub Date : 2022-06-27 DOI: 10.1090/spmj/1716
N. Abuzyarova
Four special subsets of the Schwartz algebra are defined (this algebra consists of all entire functions of exponential type and of polynomial growth on the real axis). Perturbations of the zero sets for functions belonging to each of these subsets are studied. It is shown that the boundedness of the real part of the perturbing sequence is a sufficient and, generally speaking, unimprovable condition for preservation the subset from which the function in question is taken. An application of these results to spectral synthesis problems for differentiation-invariant subspaces of the Schwartz class on an interval of the real line is considered.
定义了Schwartz代数的四个特殊子集(该代数由指数型和实轴上多项式增长的所有完整函数组成)。研究了属于这些子集的函数的零集的摄动。证明了摄动序列实部的有界性是保存所讨论的函数的子集的充分条件,一般来说,是不可改进的条件。研究了这些结果在实线区间上Schwartz类的微分不变子空间的谱合成问题中的应用。
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引用次数: 1
Positivity principle for measures on uniformly convex Banach spaces 一致凸Banach空间测度的正性原理
IF 0.8 4区 数学 Q2 MATHEMATICS Pub Date : 2022-06-27 DOI: 10.1090/spmj/1722
E. Riss

A Banach space X X is said to satisfy the positivity principle for small balls if for every finite Borel measures μ mu and ν nu on X X , the inequalities μ ( B ) ν ( B ) mu (B) leq nu (B) for all balls B of radius less than 1 imply that μ ν mu leq nu . It is shown that no uniformly convex infinite-dimensional separable Banach space X X obeys the positivity principle for small balls.

Banach空间X X被认为满足小球的正性原理,如果对于X X上的每个有限Borel测度μ,对于半径小于1的所有球B,不等式μ。证明了没有一致凸的无穷维可分Banach空间X X服从小球的正性原理。
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引用次数: 0
On interpolation and 𝐾-monotonicity for discrete local Morrey spaces 离散局部Morrey空间的插值和𝐾-monotonicity
IF 0.8 4区 数学 Q2 MATHEMATICS Pub Date : 2022-05-05 DOI: 10.1090/spmj/1707
E. Berezhnoi
A formula is given that makes it possible to reduce the calculation of an interpolation functor on a pair of local Morrey spaces to the calculation of this functor on pairs of vector function spaces constructed from the ideal spaces involved in the definition of the Morrey spaces in question. It is shown that a pair of local Morrey spaces is K K -monotone if and only if the pair of vector function spaces mentioned above is K K -monotone. This reduction makes it possible to obtain new interpolation theorems even for classical local spaces.
给出了一个公式,使插值函子在一对局部Morrey空间上的计算可以简化为该函子在由Morrey空间定义中所涉及的理想空间构造的向量函数空间对上的计算。证明了一对局部Morrey空间是K-单调的,当且仅当这对向量函数空间是K--单调的。这种约简使得即使对于经典局部空间也可以获得新的插值定理。
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引用次数: 0
期刊
St Petersburg Mathematical Journal
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